There are tons of hypothesized applications for quantum computing based on the expectation it will provide better simulation of quantum effects for e.g. chemistry, and offer major speedups of highly parallel simulation problems like nuclear plasma or some things in finance. Easy to Google to learn more about these.
But keeping the focus squarely on the military and intelligence services, one answer to your question is that everyone is not going to switch to post-quantum cryptography instantaneously. It’s going to take a while, especially for a long tail of “infrastructure” type things like networking gear, “internet of things,” industrial sensors, etc. Things that national intelligence services might like to break into to enable breaking into other things.
Quantum breaks may also still succeed against stored encrypted data from before the switch to PQ. And for at least a couple decades, national intelligence services have been scaling up their storage resources. So they might have a “backlog” they can work through.
Finally, things don’t have to last forever. Everything the military / government builds has an expected lifespan, and it only has to be valuable during that life span. And risks can be rare but huge in national security. So if quantum code-breaking computers only help the NSA learn a few very important things for a limited time, that still might be “worth it” to them. Or if a quantum computer doesn’t break any important cryptography, but helps advance the engineering and enables better quantum computers in the future for other anpplications—again, still might be worth it.